long division method of 36320
Answers
Step 1:
Divide the number (36320) by 2 to get the first guess for the square root .
First guess = 36320/2 = 18160.
Step 2:
Divide 36320 by the previous result. d = 36320/18160 = 2.
Average this value (d) with that of step 1: (2 + 18160)/2 = 9081 (new guess).
Error = new guess - previous value = 18160 - 9081 = 9079.
9079 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 36320 by the previous result. d = 36320/9081 = 3.9995595199.
Average this value (d) with that of step 2: (3.9995595199 + 9081)/2 = 4542.49977976 (new guess).
Error = new guess - previous value = 9081 - 4542.49977976 = 4538.50022024.
4538.50022024 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 36320 by the previous result. d = 36320/4542.49977976 = 7.9955975258.
Average this value (d) with that of step 3: (7.9955975258 + 4542.49977976)/2 = 2275.2476886429 (new guess).
Error = new guess - previous value = 4542.49977976 - 2275.2476886429 = 2267.2520911171.
2267.2520911171 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 36320 by the previous result. d = 36320/2275.2476886429 = 15.9630971965.
Average this value (d) with that of step 4: (15.9630971965 + 2275.2476886429)/2 = 1145.6053929197 (new guess).
Error = new guess - previous value = 2275.2476886429 - 1145.6053929197 = 1129.6422957232.
1129.6422957232 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 36320 by the previous result. d = 36320/1145.6053929197 = 31.7037613689.
Average this value (d) with that of step 5: (31.7037613689 + 1145.6053929197)/2 = 588.6545771443 (new guess).
Error = new guess - previous value = 1145.6053929197 - 588.6545771443 = 556.9508157754.
556.9508157754 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 36320 by the previous result. d = 36320/588.6545771443 = 61.7000213881.
Average this value (d) with that of step 6: (61.7000213881 + 588.6545771443)/2 = 325.1772992662 (new guess).
Error = new guess - previous value = 588.6545771443 - 325.1772992662 = 263.4772778781.
263.4772778781 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 36320 by the previous result. d = 36320/325.1772992662 = 111.6929136258.
Average this value (d) with that of step 7: (111.6929136258 + 325.1772992662)/2 = 218.435106446 (new guess).
Error = new guess - previous value = 325.1772992662 - 218.435106446 = 106.7421928202.
106.7421928202 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 36320 by the previous result. d = 36320/218.435106446 = 166.2736388438.
Average this value (d) with that of step 8: (166.2736388438 + 218.435106446)/2 = 192.3543726449 (new guess).
Error = new guess - previous value = 218.435106446 - 192.3543726449 = 26.0807338011.
26.0807338011 > 0.001. As error > accuracy, we repeat this step again.
Step 10:
Divide 36320 by the previous result. d = 36320/192.3543726449 = 188.8181667024.
Average this value (d) with that of step 9: (188.8181667024 + 192.3543726449)/2 = 190.5862696737 (new guess).
Error = new guess - previous value = 192.3543726449 - 190.5862696737 = 1.7681029712.
1.7681029712 > 0.001. As error > accuracy, we repeat this step again.
Step 11:
Divide 36320 by the previous result. d = 36320/190.5862696737 = 190.5698666655.
Average this value (d) with that of step 10: (190.5698666655 + 190.5862696737)/2 = 190.5780681696 (new guess).
Error = new guess - previous value = 190.5862696737 - 190.5780681696 = 0.0082015041.
0.0082015041 > 0.001. As error > accuracy, we repeat this step again.
Step 12:
Divide 36320 by the previous result. d = 36320/190.5780681696 = 190.5780678167.
Average this value (d) with that of step 11: (190.5780678167 + 190.5780681696)/2 = 190.5780679932 (new guess).
Error = new guess - previous value = 190.5780681696 - 190.5780679932 = 1.764e-7.
1.764e-7 <= 0.001. As error <= accuracy, we stop the iterations and use 190.5780679932 as the square root.